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A control strategy which allows to speed up the convergence of a bilinear system governed by the Fokker-Planck equation to its stationary distribution is developed. After linearization of the state equation, a linear feedback control is computed by solving the Riccati equation associated with the linearized problem. A reduction method for approximating this feedback is proposed. From a numerical point of view, this method avoids the resolution of a high-dimensional Riccati equation. Numerical results are provided for a double-well potential and the efficiency of the reduction method is demonstrated. |
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